Critical review of coupled flux formulations for clay membranes based on nonequilibrium thermodynamics

Extensive research conducted over the past several decades has indicated that semipermeable membrane behavior (i.e., the ability of a porous medium to restrict the passage of solutes) may have a significant influence on solute migration through a wide variety of clay-rich soils, including both natural clay formations (aquitards, aquicludes) and engineered clay barriers (e.g., landfill liners and vertical cutoff walls). Restricted solute migration through clay membranes generally has been described using coupled flux formulations based on nonequilibrium (irreversible) thermodynamics. However, these formulations have differed depending on the assumptions inherent in the theoretical development, resulting in some confusion regarding the applicability of the formulations. Accordingly, a critical review of coupled flux formulations for liquid, current, and solutes through a semipermeable clay membrane under isothermal conditions is undertaken with the goals of explicitly resolving differences among the formulations and illustrating the significance of the differences from theoretical and practical perspectives. Formulations based on single-solute systems (i.e., uncharged solute), single-salt systems, and general systems containing multiple cations or anions are presented. Also, expressions relating the phenomenological coefficients in the coupled flux equations to relevant soil properties (e.g., hydraulic conductivity and effective diffusion coefficient) are summarized for each system. A major difference in the formulations is shown to exist depending on whether counter diffusion or salt diffusion is assumed. This difference between counter and salt diffusion is shown to affect the interpretation of values for the effective diffusion coefficient in a clay membrane based on previously published experimental data. Solute transport theories based on both counter and salt diffusion then are used to re-evaluate previously published column test data for the same clay membrane. The results indicate that, despite the theoretical inconsistency between the counter-diffusion assumption and the salt-diffusion conditions of the experiments, the predictive ability of solute transport theory based on the assumption of counter diffusion is not significantly different from that based on the assumption of salt diffusion, provided that the input parameters used in each theory are derived under the same assumption inherent in the theory. Nonetheless, salt-diffusion theory is fundamentally correct and, therefore, is more appropriate for problems involving salt diffusion in clay membranes. Finally, the fact that solute diffusion cannot occur in an ideal or perfect membrane is not explicitly captured in any of the theoretical expressions for total solute flux in clay membranes, but rather is generally accounted for via inclusion of an effective porosity, n(e), or a restrictive tortuosity factor, tau(r), in the formulation of Fick's first law for diffusion. Both n(e) and tau(r) have been correlated as a linear function of membrane efficiency. This linear correlation is supported theoretically by pore-scale modeling of solid-liquid interactions, but experimental support is limited. Additional data are needed to bolster the validity of the linear correlation for clay membranes. Copyright 2012 Elsevier B.V. All rights reserved.

Critical Review of Coupled Flux Formulations for Clay Membranes Based on Nonequilibrium Thermodynamics

Extensive research conducted over the past several decades has indicated that semipermeable membrane behavior (i.e., the ability of a porous medium to restrict the passage of solutes) may have a significant influence on solute migration through a wide variety of clay-rich soils, including both natural clay formations (aquitards, aquicludes) and engineered clay barriers (e.g., landfill liners and vertical cutoff walls). Restricted solute migration through clay membranes generally has been described using coupled flux formulations based on nonequilibrium (irreversible) thermodynamics. However, these formulations have differed depending on the assumptions inherent in the theoretical development, resulting in some confusion regarding the applicability of the formulations. Accordingly, a critical review of coupled flux formulations for liquid, current, and solutes through a semipermeable clay membrane under isothermal conditions is undertaken with the goals of explicitly resolving differences among the formulations and illustrating the significance of the differences from theoretical and practical perspectives. Formulations based on single-solute systems (i.e., uncharged solute), single-salt systems, and general systems containing multiple cations or anions are presented. Also, expressions relating the phenomenological coefficients in the coupled flux equations to relevant soil properties (e.g., hydraulic conductivity and effective diffusion coefficient) are summarized for each system. A major difference in the formulations is shown to exist depending on whether counter diffusion or salt diffusion is assumed. This difference between counter and salt diffusion is shown to affect the interpretation of values for the effective diffusion coefficient in a clay membrane based on previously published experimental data. Solute transport theories based on both counter and salt diffusion then are used to re-evaluate previously published column test data for the same clay membrane. The results indicate that, despite the theoretical inconsistency between the counter-diffusion assumption and the salt-diffusion conditions of the experiments, the predictive ability of solute transport theory based on the assumption of counter diffusion is not significantly different from that based on the assumption of salt diffusion, provided that the input parameters used in each theory are derived under the same assumption inherent in the theory. Nonetheless, salt-diffusion theory is fundamentally correct and, therefore, is more appropriate for problems involving salt diffusion in clay membranes. Finally, the fact that solute diffusion cannot occur in an ideal or perfect membrane is not explicitly captured in any of the theoretical expressions for total solute flux in clay membranes, but rather is generally accounted for via inclusion of an effective porosity, ne, or a restrictive tortuosity factor, tr, in the formulation of Fick's first law for diffusion. Both ne and tr have been correlated as a linear function of membrane efficiency. This linear correlation is supported theoretically by pore-scale modeling of solid-liquid interactions, but experimental support is limited. Additional data are needed to bolster the validity of the linear correlation for clay membranes.

Investigation of Solid-State Shear Pulverization Processing Parameters for Polyethylene-Clay Nanocomposites

Investigates multiple processing parameters, includingpolymer type, filler type, processing technique, severity of SSSP (Solid-state shear pulverization)processing, and postprocessing, of SSSP. HDPE and LLDPE polymers with pristine clay and organo-clay samples are explored. Effects on crystallization, high-temperature behavior, mechanicalproperties, and gas barrier properties are examined. Thermal, mechanical, and morphological characterization is conducted to determine polymer/filler compatibility and superior processing methods for the polymer-clay nanocomposites.

Hoisting C Structures Into Clay In Device Drivers

This project addresses the unreliability of operating system code, in particular in device drivers. Device driver software is the interface between the operating system and the device's hardware. Device drivers are written in low level code, making them difficult to understand. Almost all device drivers are written in the programming language C which allows for direct manipulation of memory. Due to the complexity of manual movement of data, most mistakes in operating systems occur in device driver code. The programming language Clay can be used to check device driver code at compile-time. Clay does most of its error checking statically to minimize the overhead of run-time checks in order to stay competitive with C's performance time. The Clay compiler can detect a lot more types of errors than the C compiler like buffer overflows, kernel stack overflows, NULL pointer uses, freed memory uses, and aliasing errors. Clay code that successfully compiles is guaranteed to run without failing on errors that Clay can detect. Even though C is unsafe, currently most device drivers are written in it. Not only are device drivers the part of the operating system most likely to fail, they also are the largest part of the operating system. As rewriting every existing device driver in Clay by hand would be impractical, this thesis is part of a project to automate translation of existing drivers from C to Clay. Although C and Clay both allow low level manipulation of data and fill the same niche for developing low level code, they have different syntax, type systems, and paradigms. This paper explores how C can be translated into Clay. It identifies what part of C device drivers cannot be translated into Clay and what information drivers in Clay will require that C cannot provide. It also explains how these translations will occur by explaining how each C structure is represented in the compiler and how these structures are changed to represent a Clay structure.

Microscopic and Spectroscopic Methods for Probing the Clay Water Interface

Clay minerals have a fundamental importance in many processes in soils and sediments such as the bioavailability of nutrients, water retention, the adsorption of common pollutants, and the formation of an impermeable barrier upon swelling. Many of the properties of clay minerals are due to the unique environment present at the clay mineral/water interface. Traditional techniques such as X-ray diffraction (XRD) and absorption isotherms have provided a wealth of information about this interface but have suffered from limitations. The methods and results presented herein are designed to yield new experimental information about the clay mineral/water interface.A new method of studying the swelling dynamics of clay minerals was developed using in situ atomic force microscopy (AFM). The preliminary results presented here demonstrate that this technique allows one to study individual clay mineral unit layers, explore the natural heterogeneities of samples, and monitor swelling dynamics of clay minerals in real time. Cation exchange experiments were conducted monitoring the swelling change of individual nontronite quasi-crystals as the chemical composition of the surrounding environment was manipulated several times. A proof of concept study has shown that the changes in swelling are from the exchange of interlayer cations and not from the mechanical force of replacing the solution in the fluid cell. A series of attenuated total internal reflection Fourier transform infrared spectroscopy (ATR-FTIR) experiments were performed to gain a better understanding of the organization of water within the interlayer region of two Fe-bearing clay minerals. These experiments made use of the Subtractive Kramers-Kronig (SKK) Transform and the calculation of difference spectra to obtain information about interfacial water hidden within the absorption bands of bulk water. The results indicate that the reduction of structural iron disrupts the organization of water around a strongly hydrated cation such as sodium as the cation transitions from an outer-sphere complex with the mineral surface to an inner-sphere complex. In the case of a less strongly hydrated cation such as potassium, reduction of structural iron actually increases the ordering of water molecules at the mineral surface. These effects were only noticed with the reduction of iron in the tetrahedral sheet close to the basal surface where the increased charge density is localized closer to the cations in the interlayer.